Heavy Quarkonium Dynamics

TL;DR

This review surveys perturbative heavy quarkonium using non-relativistic EFTs (NRQCD, pNRQCD, vNRQCD) and the threshold expansion to separate scales m, mv, and mv^2. It details how RG-improved perturbation theory and carefully defined threshold masses address renormalon issues and stabilize predictions for top and bottom quark systems, including NNLL/NLO/NNLO cross sections, spectra, and sum-rule mass determinations. The work also contrasts the pNRQCD and vNRQCD formalisms, discusses nonperturbative regimes, and outlines remaining theoretical challenges for achieving high-precision top threshold physics and bottom-monium studies. Overall, the framework provides a principled path to precision QCD in the heavy-quark sector, with significant implications for quark masses, production rates, and spectroscopy.

Abstract

An introduction to the recent developments in perturbative heavy quarkonium physics is given. Covered are the effective theories NRQCD, pNRQCD and vNRQCD, the threshold expansion, the role of renormalons, and applications to bottom and top quark physics.

Figures (33)

• Figure 1: The two-loop NRQCD vector current correlator with the exchange of one Coulomb gluon without relativistic corrections (a) and with the kinetic energy correction indicated by the crosses (b).
• Figure 2: One-loop scalar vertex diagram with external massive lines close to threshold. Solid lines are massive, and the dashed line is massless. All lines represent scalars.
• Figure 3: NRQCD diagrams that contribute to the ${\mathbf r}\cdot{\mathbf E}$ interactions of ultrasoft gluons with the $Q\bar{Q}$ pair in pNRQCD.
• Figure 4: Graphs contributing to the three-loop IR divergence of the QCD static potential in perturbation theory.
• Figure 5: Selfenergy of a $Q\bar{Q}$ pair due to ultrasoft gluon radiation in pNRQCD.